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Properties

Label 736.2
Level 736
Weight 2
Dimension 9258
Nonzero newspaces 12
Newform subspaces 32
Sturm bound 67584
Trace bound 9

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Defining parameters

Level: \( N \) = \( 736 = 2^{5} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 32 \)
Sturm bound: \(67584\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(736))\).

Total New Old
Modular forms 17600 9678 7922
Cusp forms 16193 9258 6935
Eisenstein series 1407 420 987

Trace form

\( 9258 q - 80 q^{2} - 58 q^{3} - 80 q^{4} - 76 q^{5} - 80 q^{6} - 58 q^{7} - 80 q^{8} - 118 q^{9} + O(q^{10}) \) \( 9258 q - 80 q^{2} - 58 q^{3} - 80 q^{4} - 76 q^{5} - 80 q^{6} - 58 q^{7} - 80 q^{8} - 118 q^{9} - 96 q^{10} - 58 q^{11} - 112 q^{12} - 92 q^{13} - 112 q^{14} - 66 q^{15} - 120 q^{16} - 48 q^{17} - 120 q^{18} - 58 q^{19} - 112 q^{20} - 80 q^{21} - 104 q^{22} - 70 q^{23} - 144 q^{24} - 122 q^{25} - 40 q^{26} - 106 q^{27} - 40 q^{28} - 60 q^{29} - 16 q^{30} - 98 q^{31} - 40 q^{32} - 204 q^{33} - 56 q^{34} - 106 q^{35} - 24 q^{36} - 76 q^{37} - 96 q^{38} - 106 q^{39} - 104 q^{40} - 144 q^{41} - 120 q^{42} - 74 q^{43} - 160 q^{44} - 116 q^{45} - 116 q^{46} - 132 q^{47} - 184 q^{48} - 30 q^{49} - 160 q^{50} - 50 q^{51} - 96 q^{52} - 140 q^{53} - 104 q^{54} + 6 q^{55} - 104 q^{56} - 124 q^{57} - 72 q^{58} + 6 q^{59} - 72 q^{60} - 124 q^{61} - 40 q^{62} + 30 q^{63} - 8 q^{64} - 180 q^{65} - 32 q^{66} + 22 q^{67} - 120 q^{68} - 116 q^{69} - 144 q^{70} + 6 q^{71} - 128 q^{72} - 112 q^{73} - 112 q^{74} - 34 q^{75} - 80 q^{76} - 112 q^{77} - 160 q^{78} - 66 q^{79} - 72 q^{80} - 62 q^{81} - 80 q^{82} - 138 q^{83} - 120 q^{84} - 112 q^{85} - 40 q^{86} - 170 q^{87} - 88 q^{88} - 144 q^{89} - 104 q^{90} - 176 q^{91} - 48 q^{92} - 144 q^{93} - 104 q^{94} - 178 q^{95} - 88 q^{96} - 240 q^{97} - 40 q^{98} - 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
736.2.a \(\chi_{736}(1, \cdot)\) 736.2.a.a 2 1
736.2.a.b 2
736.2.a.c 2
736.2.a.d 2
736.2.a.e 3
736.2.a.f 3
736.2.a.g 4
736.2.a.h 4
736.2.b \(\chi_{736}(369, \cdot)\) 736.2.b.a 2 1
736.2.b.b 8
736.2.b.c 12
736.2.c \(\chi_{736}(735, \cdot)\) 736.2.c.a 24 1
736.2.h \(\chi_{736}(367, \cdot)\) 736.2.h.a 4 1
736.2.h.b 6
736.2.h.c 12
736.2.i \(\chi_{736}(183, \cdot)\) None 0 2
736.2.j \(\chi_{736}(185, \cdot)\) None 0 2
736.2.m \(\chi_{736}(93, \cdot)\) 736.2.m.a 4 4
736.2.m.b 164
736.2.m.c 184
736.2.n \(\chi_{736}(91, \cdot)\) 736.2.n.a 24 4
736.2.n.b 352
736.2.q \(\chi_{736}(193, \cdot)\) 736.2.q.a 10 10
736.2.q.b 10
736.2.q.c 20
736.2.q.d 20
736.2.q.e 60
736.2.q.f 60
736.2.q.g 60
736.2.r \(\chi_{736}(15, \cdot)\) 736.2.r.a 220 10
736.2.w \(\chi_{736}(63, \cdot)\) 736.2.w.a 240 10
736.2.x \(\chi_{736}(49, \cdot)\) 736.2.x.a 220 10
736.2.ba \(\chi_{736}(9, \cdot)\) None 0 20
736.2.bb \(\chi_{736}(7, \cdot)\) None 0 20
736.2.be \(\chi_{736}(11, \cdot)\) 736.2.be.a 3760 40
736.2.bf \(\chi_{736}(13, \cdot)\) 736.2.bf.a 3760 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(736))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(736)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)